Theresa May’s deputy has given fresh hope to second referendum campaigners by saying another vote was “perfectly practical”, according to two party leaders.

Change UK leader Heidi Allen said David Lidington, the Cabinet Office minister, had “clearly done his research” on the mechanics of a Final Say vote when she attended talks alongside Liberal Democrats Sir Vince Cable and Jo Swinson.

Sir Vince said Mr Lidington had asserted that holding another vote would be “perfectly practical” during the meeting.

In the wake of the Tories’ poor local election showing, Ms Allen said she felt there was “more of an open door” among senior Tories towards another referendum.

She told The Independent: “I set the meeting up with [David] Lidington, because I thought surely there must be a greater appetite to end this desperate madness, to get her deal through on the back of a people’s vote so we can move on.

The mood in the talks was “very different” compared with previous meetings, Ms Allen said, adding: “I sense there might have been more of an open door there.”

She said: “He was all over the detail of the legislation and how complex legislation would be, how many days of debate it might need, the timetable might look like, how it would fit around summer recess.

“He volunteered a lot of information so he has clearly done his research.”

The Independent has been campaigning for a Final Say vote on any Brexit deal – a position that has been supported by more than a million people.

Speaking after the meeting, Mr Cable told The Sun: “He was perfectly straight – he set out the government’s political position on it.

“And you have heard Theresa May say ad nauseam what a terrible idea it is.

“But it was very clear they are thinking about it, and they are doing a lot of practical planning in case it happens.

“David acknowledged that it was perfectly practical – it could be done within realistic time scales.